Abstract

Objective: The study of enzyme kinetics invariably combines mathematics, chemistry and biology. Experimental techniques allow the concentrations of species in an in vitro reaction to be measured in real time. Numerical fitting algorithms can then be used to estimate unknown parameters for a given mathematical model. Structural identifiability analysis of the model is essential to discover whether the parameters could be uniquely determined (or otherwise) from a perfect noise-free form of the data collected. By analysing models corresponding to changes of experimental technique it is possible to design experiments which produce data appropriate for robust numerical fitting.

Result: Three experimental approaches to studying a simple two substrate enzyme catalysed reaction were considered. The first case, using quasi-steady state assumptions and measurement of reaction product only, proved unidentifiable using a variant of the Taylor series approach. Of the four unknown parameters only one was identifiable. The second case, an experiment measuring reaction product and an intermediate for a complete time series, was found to be identifiable using the Taylor series approach. The third case, an alternative experiment for the second case without the measurement of an intermediate, proved intractable using the same approach. However use of a novel input/output relationship approach showed this model to be identifiable.

Conclusions: Typical experimental procedure for enzyme kinetics measures steady state concentrations of reaction product. A single time course of such measurements are insufficient for numerical fitting to uniquely estimate the unknown parameters for the relatively simple model considered. These results suggest that a change of experimental technique to measure pre-steady state concentrations is necessary to allow accurate parameter estimation. Additionally a new input/output relationship approach to structural identifiability analysis has been developed which proves effective in cases where the Taylor series approach is unable to produce a result.